The issue is that given the same set of circumstances, a black person is more likely to be searched/shot/whatever than a white person. In the case of police shootings, yes some white dudes have been shot as well as black dudes. But if you look at all the cases of police shootings in the FBI database and compare the cases of white dudes waving knives at cops vs the sample of black dudes waving knives at cops, the police are N times more likely to shoot and kill the the black dudes. (I can't recall exactly what N is but I think it was 5 or 6).
If you're going to "burst bubbles" when talking about privilege, I encourage you to learn about intersectionality first. Otherwise you're bursting a straw man version of the concept, which doesn't achieve anything. Privilege exists on multiple axes, and you still have white privilege even if you're poor and don't have class privilege.